We construct a 2D synthetic problem by setting \(f(x)\)  to be a four-branch function (that has been widely-used in estimating extreme-event probability with a deterministic ItR) [1]}, [2]}, [3]}, [4]}:
\(f(x_1, x_2) = - {\rm {min}}\left\lbrace \begin{aligned}& 8+ 0.1(x_1-x_2)^2 + \frac{(x_1 + x_2)}{\sqrt{2}} \\& 8+ 0.1(x_1-x_2)^2 - \frac{(x_1 + x_2)}{\sqrt{2}} \\& (x_1 - x_2) + \frac{6}{\sqrt{2}} + 5 \\& (x_2 - x_1) + \frac{6}{\sqrt{2}} + 5 \\\end{aligned}\right..\) 
